I propose having a rivals list for the players you really want to play against.
Specifics:
Create a rivals list similar to that of a friends list. But the rivals list should used for search criteria when you are looking for a game. That way, if the player has started or has joined a game, you can join in to play them. Also, place the rivals at the top of the search list that way they are easy to find.
This will improve the following aspects of the site:
Players would be able to play against that player who gave them a really tough match/beat them and wanted to get a rematch with.
As far as I know, your friend's list isn't used in search criteria. Besides, some of them may not be your friend, they just may be someone you want a rematch again.
